The group \(G\)  then naturally acts on the homogeneous coordinate ring \(S\)  of \(\mathbb {P}^2\) . An important characteristic of comflex reflection groups is that the invariant ring of such groups is finitely generated [1]}. Let \(G=A_5\times \mathbb {Z} _2\)  The invariant ring \(S^G\)  is generated as a \(-algebra by homogeneous forms \) 2,6,10\( where the subscript denotes the degree of the form. The polynomials \) d\( turn out to be vital in considering curves vanishing to points of the point configuration. This will allow us to construct curves of high multiplicities at the singularities of \) A\( in order to bound \) (IA)\( from above.\)
